Prentice Hall Connected Mathematics 2, 7th Grade Units 2009
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1 Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O Idaho Content Standards, Grade 7 Mathematics
2 Introduction The Correlation of Connected Mathematics 2 (CMP2), 7 th Grade Units 2009 to the Idaho Content Standards, Grade 7 Mathematics, demonstrates the alignment of content between CMP2 and the Idaho Content Standards. This document contains references from the Teacher Guides (TG) and Student Editions (SE) to the relevant standards in Grade 7 Mathematics. Additional Topics that will be available on Pearson SuccessNet were added to this correlation to further enhance the alignment of CMP2 to the Idaho Content Standards. As part of the CMP2 program, teachers also have these resources to draw from for professional development, support for parents and students, assessment, and practice. Additional CMP2 Teacher Resources include: Implementing and Teaching Guide, Strategies for English Language Learners, Parent Guide, Special Needs Handbook, Teaching Transparencies, Grade 7 Additional Practice and Skills Workbook, Grade 7 Assessment Resources Additional CMP2Technology Resources include: StudentEXPRESS CD-ROM, ExamView 6.0 Test Bank CD-ROM, TeacherSTATION (includes Teacher Express, MindPoint QuizShow and Presentation Resources), Teaching Middle Grades with TI Technology, Success Tracker, and pearsonschool.com The National Science Foundation funded Connected Mathematics Project between 1991 and 1997 to develop a middle school mathematics program. That program, Connected Mathematics, was a complete mathematics curriculum to help students develop understanding of important concepts, skills, procedures, and ways of thinking and reasoning in number, geometry, measurement, algebra, probability, and statistics. The National Science Foundation funded a revision of Connected Mathematics in This revision, CMP2 took advantage of lessons learned in the six years that the first edition was used in classrooms. With the introduction of CMP2, it is important to note that for more than five years, the authors worked to build on the solid foundation already established by the first CMP and the research supporting the program. Research has been the central, guiding force in the product development process. Authors and product developers relied on the efficacy data for making improvements in design and content, resulting in an even more effective program. Fifteen sites, with varying characteristics that are representative of schools across the nation, participated in three rounds of revisions for each grade level. Input from more than 15,000 students and 300 teachers was integrated into CMP2. CMP2 has already proven to support student learning, helps students to develop and maintain their skills, and enhances their mathematical thinking and reasoning. Connected Mathematics 2 provides 24 Student Units (8 per grade level). Every unit develops a big mathematical idea, important clusters of related concepts, skills, procedures, and ways of thinking. Students develop understanding of algorithms and strategies for computing and estimating in a variety of ways. They learn to recognize when an algorithm or strategy applies to a new context and when they can build on the skills and strategies they know in order to develop new strategies. In these processes, students practice skills as an ongoing activity throughout the curriculum. In addition, Connected Mathematics 2 helps students develop algebraic reasoning. The program aims to expand student views of algebra beyond symbolic manipulation and offers opportunities for students to apply algebraic reasoning to problems in many different contexts throughout the course of the curriculum. 1
3 Standard 1: Number and Operation Goal 1.1: Understand and use numbers. Objective 1: 7.M Compare magnitudes and relative magnitudes of rational numbers, including integers, fractions, and decimals. ( a, c) Objective 2: 7.M Solve problems requiring the conversion between simple decimals, fractions, ratios, and percents. ( b) Objective 3: 7.M Locate the position of rational numbers on a number line. ( e) Objective 4: 7.M Rewrite multiples factors using exponents. ( c) SE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (23), Stretching and Shrinking Investigation 3: Similar Polygons (51), Investigation 5: Using Similar Triangles and Rectangles (85), Comparing and Scaling Investigation 1: Making Comparisons (15), Investigation 2: Comparing Ratios, Percents, and Fractions (26-28), Accentuate the Negative Investigation 1: Extending the Number System (5-21), Investigation 4: Properties of Operations (72, 74) TG: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (40), Stretching and Shrinking Investigation 3: Similar Polygons (70), Investigation 5: Using Similar Triangles and Rectangles (103), Comparing and Scaling Investigation 1: Making Comparisons (29), Investigation 2: Comparing Ratios, Percents, and Fractions (48), Accentuate the Negative Investigation 1: Extending the Number System (15-35), Investigation 4: Properties of Operations ( ) SE: Comparing and Scaling Investigation 2: Comparing Ratios, Percents, and Fractions (20-21, 25-28, 30) TG: Comparing and Scaling Investigation 2: Comparing Ratios, Percents, and Fractions (39-42, 47-48, 50) SE: Comparing and Scaling Investigation 1: Making Comparisons (14), Accentuate the Negative Investigation 1: Extending the Number System (10-13, 16-18), Investigation 4: Properties of Operations (72-73) TG: Comparing and Scaling Investigation 1: Making Comparisons (28), Accentuate the Negative Investigation 1: Extending the Number System (21-28, 33-34), Investigation 4: Properties of Operations ( ) Online Activities: NO-a Prime Factorization, NO-c Rules of Exponents 2
4 Objective 5: 7.M Apply the number theory concepts of primes, composites, and prime factorization and find the Least common Multiple (LCM) and the Greatest Common Factor (GCF). ( d) SE: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (48-49, 53) Objective 6: 7.M Recognize pertinent information for problem solving. ( b) Objective 7: 7.M Describe the use of integers in real-world situations. Objective 8: 7.M Use appropriate vocabulary. Goal 1.2: Perform computations accurately. Objective 1: 7.M Recall the common equivalent fractions, decimals, and percents of halves, fourths, and tenths. TG: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (77-80, 82) Online Activity: NO-a Prime Factorization SE: Accentuate the Negative Investigation 1: Extending the Number System (5-21) TG: Accentuate the Negative Investigation 1: Extending the Number System (15-35) Online Activity: GM-y Deductive Reasoning SE: Accentuate the Negative Investigation 1: Extending the Number System (8-13, 17, 19-20), Investigation 2: Adding and Subtracting Integers (37-38, 40), Investigation 3: Multiplying and Dividing Integers (50, 53, 55-56), Investigation 4: Properties of Operations (66-67, 71-73) TG: Accentuate the Negative Investigation 1: Extending the Number System (15-28, 34-35), Investigation 2: Adding and Subtracting Integers (59, 61), Investigation 3: Multiplying and Dividing Integers (81-84), Investigation 4: Properties of Operations (95-98, ) SE: Accentuate the Negative Investigation 1: Extending the Number System (21), Investigation 2: Adding and Subtracting Integers (24-27, 41), Investigation 3: Multiplying and Dividing Integers (59), Investigation 4: Properties of Operations (75) TG: Accentuate the Negative Investigation 1: Extending the Number System (35), Investigation 2: Adding and Subtracting Integers (41-44, 61), Investigation 3: Multiplying and Dividing Integers (85), Investigation 4: Properties of Operations (101) SE: Comparing and Scaling Investigation 2: Comparing Ratios, Percents, and Fractions (18-32) TG: Comparing and Scaling Investigation 2: Comparing Ratios, Percents, and Fractions (32-50) 3
5 Objective 2: 7.M Add, subtract, multiply, and divide whole numbers, fractions and decimals; and add, multiply and divide integers. ( a, d) Objective 3: 7.M Evaluate whole numbers in exponential form. Objective 4: 7.M Evaluate numerical expressions using the order of operations with whole numbers and decimals. ( b) Objective 5: 7.M Select and use an appropriate method of computation from mental math, paper and pencil, calculator, or a combination of the three. ( e) SE: Stretching and Shrinking Investigation 2: Similar Figures (34), Accentuate the Negative Investigation 1: Extending the Number System (12-15, 17-20), Investigation 2: Adding and Subtracting Integers (22-41), Investigation 3: Multiplying and Dividing Integers (42-59), Investigation 4: Properties of Operations (70-71), Moving Straight Ahead Investigation 3: Solving Equations (64) TG: Stretching and Shrinking Investigation 2: Similar Figures (52), Accentuate the Negative Investigation 1: Extending the Number System (25-35), Investigation 2: Adding and Subtracting Integers (37-61), Investigation 3: Multiplying and Dividing Integers (62-85), Investigation 4: Properties of Operations (100), Moving Straight Ahead Investigation 3: Solving Equations (92) SE: Accentuate the Negative Investigation 4: Properties of Operations (60-75) TG: Accentuate the Negative Investigation 4: Properties of Operations (87-102) Online Activity: AL-g Evaluating Algebraic Expressions SE: Accentuate the Negative Investigation 4: Properties of Operations (60-75) TG: Accentuate the Negative Investigation 4: Properties of Operations (87-102) Online Activity: AL-g Evaluating Algebraic Expressions SE: Accentuate the Negative Investigation 2: Adding and Subtracting Integers (32-35), Investigation 3: Multiplying and Dividing Integers (55) Related Content: Stretching and Shrinking Investigation 2: Similar Figures (34), Accentuate the Negative Investigation 1: Extending the Number System (12-15, 17-20), Investigation 2: Adding and Subtracting Integers (22-41), Investigation 3: Multiplying and Dividing Integers (42-59), Investigation 4: Properties of Operations (70-71), Moving Straight Ahead Investigation 3: Solving Equations (64) 4
6 Objective 6: 7.M Use a variety of strategies including common mathematical formulas to compute problems drawn from reallife situations. ( a) TG: Accentuate the Negative Investigation 2: Adding and Subtracting Integers (57-59), Investigation 3: Multiplying and Dividing Integers (84) Related Content: Stretching and Shrinking Investigation 2: Similar Figures (52), Accentuate the Negative Investigation 1: Extending the Number System (25-35), Investigation 2: Adding and Subtracting Integers (37-61), Investigation 3: Multiplying and Dividing Integers (62-85), Investigation 4: Properties of Operations (100), Moving Straight Ahead Investigation 3: Solving Equations (92) SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (5-6, 12-14, 16-17), Investigation 2: Similar Figures (34-35), Investigation 4: Similarity and Ratios (69-72, 74), Rectangles (78-79, 84-85, 88-92), Accentuate the Negative Investigation 2: Adding and Subtracting Integers (37-38, 40), Investigation 3: Multiplying and Dividing Integers (50, 53, 55-56), Investigation 4: Properties of Operations (66-67, 71-73), Filling and Wrapping Investigation 1: Building Boxes (15-16), Investigation 2: Designing Rectangular Boxes (20, 22-24, 28-30), Investigation 3: Prisms and Cylinders (37, 39, 42-43, 45), Investigation 4: Cones, Spheres, and Pyramids (52-53, 57-59), Investigation 5: Scaling Boxes (63-66, 68-74), Unit Project (76-77), Looking Back and Looking Ahead (78-80) TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (15-18, 29-30), Investigation 2: Similar Figures (52), Investigation 4: Similarity and Ratios (88-89), Rectangles (91-94, ), Accentuate the Negative Investigation 2: Adding and Subtracting Integers (59, 61), Investigation 3: Multiplying and Dividing Integers (81-84), Investigation 4: Properties of Operations (95-98, ), Filling and Wrapping Investigation 1: Building Boxes (34), Investigation 2: Designing Rectangular Boxes (37-42, 47-54), Investigation 3: Prisms and Cylinders (69-76), Investigation 4: Cones, Spheres, and Pyramids (87-90, 92-93), Investigation 5: Scaling Boxes (96-108, ), Unit Project ( ), Looking Back and Looking Ahead ( ) 5
7 Objective 7: 7.M Use appropriate vocabulary and notations. ( f) Goal 1.3: Estimate and judge reasonableness of results. Objective 1: 7.M Estimate to predict computation results. ( a) Objective 2: 7.M Explain when estimation is appropriate and describe the usefulness of an estimate as opposed to an exact answer. ( b) Objective 3: 7.M Identify whether a given estimate is an overestimate or underestimate. ( c) Objective 4: 7.M Use a four-function calculator to solve complex grade-level problems. SE: Accentuate the Negative Investigation 2: Adding and Subtracting Integers (24-27, 41), Investigation 3: Multiplying and Dividing Integers (59), Investigation 4: Properties of Operations (75), Filling and Wrapping Investigation 1: Building Boxes (18), Investigation 2: Designing Rectangular Boxes (20, 31), Investigation 3: Prisms and Cylinders (34-35, 47), Investigation 4: Cones, Spheres, and Pyramids (61), Investigation 5: Scaling Boxes (75), Unit Project (76-77), Looking Back and Looking Ahead (78-80) TG: Accentuate the Negative Investigation 2: Adding and Subtracting Integers (41-44, 61), Investigation 3: Multiplying and Dividing Integers (85), Investigation 4: Properties of Operations (101), Filling and Wrapping Investigation 1: Building Boxes (35), Investigation 2: Designing Rectangular Boxes (37-42, 54), Investigation 3: Prisms and Cylinders (61-64, 77), Investigation 4: Cones, Spheres, and Pyramids (94), Investigation 5: Scaling Boxes (112), Unit Project ( ), Looking Back and Looking Ahead ( ) SE: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (42-59) TG: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (62-85) Online Activity: NO-l Multiplying and Dividing Rational Numbers An opportunity to address this standard can be found on: SE: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (42-59) TG: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (62-85) An opportunity to address this standard can be found on: SE: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (42-59) TG: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (62-85) Online Activity: NO-l Multiplying and Dividing Rational Numbers SE: Variables and Patterns Investigation 4: Calculator Tables and Graphs (64-80) 6
8 Objective 5: 7.M Formulate conjectures and discuss why they must be or seem to be true. ( c) Objective 6: 7.M Use appropriate vocabulary and notations. ( d) TG: Variables and Patterns Investigation 4: Calculator Tables and Graphs (87-102) SE: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (59) TG: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (85) Online Activities: GM-x Inductive Reasoning, GM-y Deductive Reasoning SE: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (59) Standard 2: Concepts and Principles of Measurement TG: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (85) Online Activities: GM-x Inductive Reasoning, GM-y Deductive Reasoning Goal 2.1: Understand and use U.S. customary and metric measurements. Objective 1: 7.M Select and use appropriate units and tools to make formal measurements in both systems. ( a) Objective 2: 7.M Apply estimation of measurement to real-world and content problems using standard measuring devices. ( b) SE: Filling and Wrapping Investigation 1: Building Boxes (5-18), Investigation 2: Designing Rectangular Boxes (19-31), Investigation 3: Prisms and Cylinders (48-61), Investigation 4: Cones, Spheres, and Pyramids (62-75), Investigation 5: Scaling Boxes (62-75), Unit Project (76-77), Looking Back and Looking Ahead (78-80) TG: Filling and Wrapping Investigation 1: Building Boxes (14-35), Investigation 2: Designing Rectangular Boxes (37-54), Investigation 3: Prisms and Cylinders (57-77), Investigation 4: Cones, Spheres, and Pyramids (79-94), Investigation 5: Scaling Boxes (96-112), Unit Project ( ), Looking Back and Looking Ahead ( ) SE: Filling and Wrapping Investigation 2: Designing Rectangular Boxes (24), Investigation 3: Prisms and Cylinders (43), Investigation 4: Cones, Spheres, and Pyramids (55) TG: Filling and Wrapping Investigation 2: Designing Rectangular Boxes (51), Investigation 3: Prisms and Cylinders (75), Investigation 4: Cones, Spheres, and Pyramids (92) Online Activities: ME-a Using Fractions of an Inch and Converting Measurements, ME-c Accurate and Precise Measurements 7
9 Objective 3: 7.M Explain the differences between perimeter, area, and volume (capacity) and their measures within both systems. ( c) Objective 4: 7.M Given the formulas, find the perimeter, circumference, or area of triangles, circles, and quadrilaterals. ( e) Objective 5: 7.M Convert units of measurement within each system. ( e) Objective 6: 7.M Solve problems involving perimeter and area of rectangles and triangles. ( d) An opportunity to address this standard can be found on: SE: Filling and Wrapping Investigation 1: Building Boxes (5-18), Investigation 2: Designing Rectangular Boxes (19-31), Investigation 3: Prisms and Cylinders (48-61), Investigation 4: Cones, Spheres, and Pyramids (62-75), Investigation 5: Scaling Boxes (62-75) TG: Filling and Wrapping Investigation 1: Building Boxes (14-35), Investigation 2: Designing Rectangular Boxes (37-54), Investigation 3: Prisms and Cylinders (57-77), Investigation 4: Cones, Spheres, and Pyramids (79-94), Investigation 5: Scaling Boxes (96-112) SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (7-19), Investigation 2: Similar Figures (25-36), Investigation 3: Similar Polygons (38-57), Investigation 4: Similarity and Ratios (68-69), Rectangles (86-87, 89, 92) TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (19-31), Investigation 2: Similar Figures (43-53), Investigation 3: Similar Polygons (55-73), Investigation 4: Similarity and Ratios (88), Rectangles ( ) SE: Stretching and Shrinking Investigation 4: Similarity and Ratios (69), Filling and Wrapping Investigation 4: Scaling Boxes (70, 72) TG: Stretching and Shrinking Investigation 4: Similarity and Ratios (88), Filling and Wrapping Investigation 4: Scaling Boxes (111) Online Activities: ME-a Using Fractions of an Inch and Converting Measurements, ME-b Conversion Factors, ME-d Dimensional Analysis SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (7-19), Investigation 2: Similar Figures (25-36), Investigation 3: Similar Polygons (38-57), Investigation 4: Similarity and Ratios (68-69), Rectangles (86-87, 89) 8
10 Objective 7: 7.M Use appropriate vocabulary and notations. ( f) Goal 2.2: Apply the concepts of rates, ratios, and proportions. Objective 1: 7.M Explain rates and their relationship to ratios, and use proportions to solve problems represented with a diagram. ( a, a) TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (19-31), Investigation 2: Similar Figures (43-53), Investigation 3: Similar Polygons (55-73), Investigation 4: Similarity and Ratios (88), Rectangles ( ) SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (20), Investigation 2: Similar Figures (37), Investigation 3: Similar Polygons (57), Investigation 4: Similarity and Ratios (77), Rectangles (80-81, 93), Filling and Wrapping Investigation 1: Building Boxes (18), Investigation 2: Designing Rectangular Boxes (20, 31), Investigation 3: Prisms and Cylinders (34-35, 47), Investigation 4: Cones, Spheres, and Pyramids (61), Investigation 5: Scaling Boxes (75), Unit Project (76-77), Looking Back and Looking Ahead (78-80) TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (31), Investigation 2: Similar Figures (53), Investigation 3: Similar Polygons (73), Investigation 4: Similarity and Ratios (89), Rectangles (95-98, ), Filling and Wrapping Investigation 1: Building Boxes (35), Investigation 2: Designing Rectangular Boxes (37-42, 54), Investigation 3: Prisms and Cylinders (61-64, 77), Investigation 4: Cones, Spheres, and Pyramids (94), Investigation 5: Scaling Boxes (112), Unit Project ( ), Looking Back and Looking Ahead ( ) SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (15-16), Investigation 3: Similar Polygons (42-43, 47-49, 53, 56), Investigation 4: Similarity and Ratios (58-77), Investigation 5: Using Similar Triangles and Rectangles (78-93), Comparing and Scaling Investigation 1: Making Comparisons (13), Investigation 3: Comparing and Scaling Rates (33-47), Investigation 4: Making Sense of Proportions (49-51, 55, 57-59) Related Content: Comparing and Scaling Looking Back and Looking Ahead (65-67) 9
11 Objective 2: 7.M Reduce rates to unit rates. Goal 2.3: Apply dimensional analysis. Objective 1: 7.M Identify properly constructed dimensional analysis conversions. ( a) TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (30), Investigation 3: Similar Polygons (65-68, 70-72), Investigation 4: Similarity and Ratios (75-89), Rectangles (91-106), Comparing and Scaling Investigation 1: Making Comparisons (28), Investigation 3: Comparing and Scaling Rates (52-72), Investigation 4: Making Sense of Proportions (74-78, 89-91) Related Content: Comparing and Scaling Looking Back and Looking Ahead (92-93) SE: Comparing and Scaling Investigation 3: Comparing and Scaling Rates (33-34, 36-39, 42, 45, 47), Investigation 4: Making Sense of Proportions (55, 57) TG: Comparing and Scaling Investigation 3: Comparing and Scaling Rates (52-56, 61-68, 71-72), Investigation 4: Making Sense of Proportions (89-90) Online Activity: AL-p Unit Rates Online Activity: ME-d Dimensional Analysis An opportunity to further address this standard can be found on: SE: Comparing and Scaling Investigation 3: Comparing and Scaling Rates (45) TG: Comparing and Scaling Investigation 3: Comparing and Scaling Rates (71) Online Activities: ME-a Using Fractions of an Inch and Converting Measurements, ME-b Conversion Factors, ME-c Accurate and Precise Measurements Standard 3: Concepts and Language of Algebra and Functions Goal 3.1: Use algebraic symbolism as a tool to represent mathematical relationships. Objective 1: 7.M Use variables in simple expressions and equations. ( a) SE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (5-29), Investigation 2: Analyzing Graphs and Tables (30-48), Investigation 3: Rules and Equations (49-63), Investigation 4: Calculator Tables and Graphs (64-80), Looking Back and Looking Ahead (81-83), Comparing and Scaling Investigation 3: Comparing and Scaling Rates (33-34, 36-37, 40-42, 45-46) 10
12 Objective 2: 7.M Translate simple word statements into algebraic expressions and equations. ( b) Objective 3: 7.M Use symbols <, >, =,,, and, to express relationships. ( c) Goal 3.2: Evaluate algebraic expressions. Objective 1: 7.M Evaluate simple numeric and algebraic expressions using commutative, associative, identity, zero, inverse, distributive, and substitution properties. ( a) Objective 2: 7.M Use the order of operations in evaluating simple algebraic expressions. ( b) TG: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (16-43), Investigation 2: Analyzing Graphs and Tables (45-67), Investigation 3: Rules and Equations (69-85), Investigation 4: Calculator Tables and Graphs (87-102), Looking Back and Looking Ahead ( ), Comparing and Scaling Investigation 3: Comparing and Scaling Rates (52-56, 61-64, 69-72) SE: Variables and Patterns Investigation 3: Rules and Equations (49-63), Investigation 4: Calculator Tables and Graphs (74-75, 79) TG: Variables and Patterns Investigation 3: Rules and Equations (69-85), Investigation 4: Calculator Tables and Graphs (100, 102) SE: Stretching and Shrinking Investigation 5: Using Similar Triangles and Rectangles (85), Moving Straight Ahead Investigation 2: Exploring Linear Functions With Graphs and Tables (41-42), Investigation 3: Solving Equations (46-69) TG: Stretching and Shrinking Investigation 5: Using Similar Triangles and Rectangles (103), Moving Straight Ahead Investigation 2: Exploring Linear Functions With Graphs and Tables (64), Investigation 3: Solving Equations (67-94) Online Activities: AL-c Writing and Solving Inequalities, AL-r Inequalities SE: Accentuate the Negative Investigation 4: Properties of Operations (60-75), Moving Straight Ahead Investigation 3: Solving Equations (46-69) TG: Accentuate the Negative Investigation 4: Properties of Operations (87-102), Moving Straight Ahead Investigation 3: Solving Equations (67-94) SE: Accentuate the Negative Investigation 4: Properties of Operations (60-75), Moving Straight Ahead Investigation 3: Solving Equations (46-69) TG: Accentuate the Negative Investigation 4: Properties of Operations (87-102), Moving Straight Ahead Investigation 3: Solving Equations (67-94) 11
13 Goal 3.3: Solve algebraic equations and inequalities. Objective 1: 7.M Solve one-step equations. ( a) Goal 3.4: Understand the concept of functions. Objective 1: 7.M Extend patterns involving rational numbers and describe the rule that generates the pattern. ( a) Objective 2: 7.M Explain how a change in one quantity impacts a change in another quantity. ( b) Objective 3: 7.M Use appropriate vocabulary and notations. ( c) SE: Accentuate the Negative Investigation 2: Adding and Subtracting Integers (39), Investigation 3: Multiplying and Dividing Integers (52), Investigation 4: Properties of Operations (71) Related Content: Moving Straight Ahead Investigation 3: Solving Equations (46-69) TG: Accentuate the Negative Investigation 2: Adding and Subtracting Integers (61), Investigation 3: Multiplying and Dividing Integers (81), Investigation 4: Properties of Operations (100) Related Content: Moving Straight Ahead Investigation 3: Solving Equations (67-94) SE: Variables and Patterns Investigation 2: Analyzing Graphs and Tables (30-48), Investigation 3: Rules and Equations (49-63), Investigation 4: Calculator Tables and Graphs (64-80), Looking Back and Looking Ahead (81-83) TG: Variables and Patterns Investigation 2: Analyzing Graphs and Tables (45-67), Investigation 3: Rules and Equations (69-85), Investigation 4: Calculator Tables and Graphs (87-102), Looking Back and Looking Ahead ( ) SE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (5-29), Investigation 2: Analyzing Graphs and Tables (30-48), Investigation 3: Rules and Equations (49-63), Investigation 4: Calculator Tables and Graphs (64-80) TG: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (16-43), Investigation 2: Analyzing Graphs and Tables (45-67), Investigation 3: Rules and Equations (69-85), Investigation 4: Calculator Tables and Graphs (87-102) SE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (12-13, 29), Investigation 2: Analyzing Graphs and Tables (32, 48), Investigation 3: Rules and Equations (63), Investigation 4: Calculator Tables and Graphs (80), Looking Back and Looking Ahead (81-83) 12
14 TG: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (29-32, 43), Investigation 2: Analyzing Graphs and Tables (51-54, 67), Investigation 3: Rules and Equations (85), Investigation 4: Calculator Tables and Graphs (102), Looking Back and Looking Ahead ( ) Goal 3.5: Represent equations, inequalities and functions in a variety of formats. Objective 1: 7.M Represent a simple set of data in a table, as a graph, and as a mathematical relationship. ( a) Goal 3.6: Apply functions to a variety of problems. Objective 1: 7.M Use patterns and linear functions to represent and solve simple problems. ( a) SE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (5-29), Investigation 2: Analyzing Graphs and Tables (30-48), Investigation 3: Rules and Equations (49-63), Investigation 4: Calculator Tables and Graphs (64-80), Looking Back and Looking Ahead (81-83), Comparing and Scaling Investigation 2: Comparing Ratios, Percents, and Fractions (29), Moving Straight Ahead Investigation 1: Walking Rates (5-23), Investigation 2: Exploring Linear Functions With Graphs and Tables (24-45), Investigation 3: Solving Equations (46-69), Investigation 4: Exploring Slope (70-89), Unit Project (90-93), Looking Back and Looking Ahead (94-96) TG: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (16-43), Investigation 2: Analyzing Graphs and Tables (45-67), Investigation 3: Rules and Equations (69-85), Investigation 4: Calculator Tables and Graphs (87-102), Looking Back and Looking Ahead ( ), Comparing and Scaling Investigation 2: Comparing Ratios, Percents, and Fractions (49), Moving Straight Ahead Investigation 1: Walking Rates (16-40), Investigation 2: Exploring Linear Functions With Graphs and Tables (42-65), Investigation 3: Solving Equations (67-94), Investigation 4: Exploring Slope (96-120), Unit Project ( ), Looking Back and Looking Ahead ( ) SE: Moving Straight Ahead Investigation 1: Walking Rates (5-23), Investigation 2: Exploring Linear Functions With Graphs and Tables (24-45), Investigation 3: Solving Equations (46-69), Investigation 4: Exploring Slope (70-89), Unit Project (90-93), Looking Back and Looking Ahead (94-96) 13
15 Standard 4: Concepts and Principles of Geometry Goal 4.1: Apply concepts of size, shape, and spatial relationships. Objective 1: 7.M Classify relationships among types of one- and two-dimensional geometric figures, using their defining properties. ( a) Objective 2: 7.M Draw and measure various angles and shapes using appropriate tools. ( b) Objective 3: 7.M Apply fundamental concepts, properties, and relationships among points, lines, rays, plans, and angles. ( c) TG: Moving Straight Ahead Investigation 1: Walking Rates (16-40), Investigation 2: Exploring Linear Functions With Graphs and Tables (42-65), Investigation 3: Solving Equations (67-94), Investigation 4: Exploring Slope (96-120), Unit Project ( ), Looking Back and Looking Ahead ( ) SE: Stretching and Shrinking Investigation 2: Similar Figures (24-27, 29-36), Investigation 3: Similar Polygons (39-41, 44-46, 53-54), Investigation 4: Similarity and Ratios (58-77), Rectangles (78-93), Unit Project (94-97), Looking Back and Looking Ahead (98-100) TE: Stretching and Shrinking Investigation 2: Similar Figures (39-48, 50-53), Investigation 3: Similar Polygons (55-60, 69-72), Investigation 4: Similarity and Ratios (75-89), Investigation 5: Using Similar Triangles and Rectangles (91-106), Unit Project ( ), Looking Back and Looking Ahead (105) SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (7-9, 13, 15, 19), Investigation 2: Similar Figures (21-37), Investigation 3: Similar Polygons (38-57), Investigation 4: Similarity and Ratios (67, 74-75), Rectangles (78-81) TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (19-24, 29-31), Investigation 2: Similar Figures (33-53), Investigation 3: Similar Polygons (55-73), Investigation 4: Similarity and Ratios (87, 89), Rectangles (91-98) SE: Stretching and Shrinking Investigation 3: Similar Polygons (42-43, 48-50), Investigation 4: Similarity and Ratios (58-77), Investigation 5: Using Similar Triangles and Rectangles (78-93) TG: Stretching and Shrinking Investigation 3: Similar Polygons (65-68, 70), Investigation 4: Similarity and Ratios (75-89), Investigation 5: Using Similar Triangles and Rectangles (91-106) 14
16 Objective 4: 7.M Explain and model the effects of reflections, translations, and rotations on various shapes. ( g) Objective 5: 7.M Identify congruence, similarities, and line symmetry of shapes. ( d) Objective 6: 7.M Describe the concept of surface area and volume (capacity). ( f) Objective 7: 7.M Use appropriate vocabulary and symbols. ( h) SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (5-20), Investigation 2: Similar Figures (21-37), Looking Back and Looking Ahead (98-100), Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (54, 57) TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (15-31), Investigation 2: Similar Figures (33-53), Looking Back and Looking Ahead (105), Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (83-84) SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (5-20), Investigation 2: Similar Figures (21-37), Investigation 3: Similar Polygons (38-57), Rectangles (78-93), Unit Project (94-97), Looking Back and Looking Ahead (98-100) TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (15-31), Investigation 2: Similar Figures (33-53), Investigation 3: Similar Polygons (55-73), Rectangles (91-106), Unit Project ( ), Looking Back and Looking Ahead (105) SE: Filling and Wrapping Investigation 2: Designing Rectangular Boxes (19-31), Investigation 3: Prisms and Cylinders (48-61), Investigation 4: Cones, Spheres, and Pyramids (62-75) TG: Filling and Wrapping Investigation 2: Designing Rectangular Boxes (37-54), Investigation 3: Prisms and Cylinders (57-77), Investigation 4: Cones, Spheres, and Pyramids (79-94) SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (20), Investigation 2: Similar Figures (37), Investigation 3: Similar Polygons (57), Investigation 4: Similarity and Ratios (77), Rectangles (80-81, 93), Unit Project (94-97), Looking Back and Looking Ahead (98-100), Filling and Wrapping Investigation 2: Designing Rectangular Boxes (20, 31), Investigation 3: Prisms and Cylinders (34-35, 47), Investigation 4: Cones, Spheres, and Pyramids (61) 15
17 Goal 4.2: Apply the geometry of right triangles. No objectives at this grade level. Goal 4.3: Apply graphing in two dimensions. Objective 1: 7.M Identify and plot points on a coordinate plan. TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (31), Investigation 2: Similar Figures (53), Investigation 3: Similar Polygons (73), Investigation 4: Similarity and Ratios (89), Rectangles (95-98, ), Unit Project ( ), Looking Back and Looking Ahead (105), Filling and Wrapping Investigation 2: Designing Rectangular Boxes (37-42, 54), Investigation 3: Prisms and Cylinders (61-64, 77), Investigation 4: Cones, Spheres, and Pyramids (94) SE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (5-29), Investigation 2: Analyzing Graphs and Tables (30-48), Investigation 4: Calculator Tables and Graphs (64-80), Stretching and Shrinking Investigation 2: Similar Figures (22-25, 28-29, 31-36), Comparing and Scaling Investigation 2: Comparing Ratios, Percents, and Fractions (29), Investigation 4: Making Sense of Proportions (57-58), Accentuate the Negative Investigation 2: Adding and Subtracting Integers (30-31, 36-37, 39), Moving Straight Ahead Investigation 1: Walking Rates (5-23), Investigation 2: Exploring Linear Functions With Graphs and Tables (24-45), Investigation 3: Solving Equations (46-69), Investigation 4: Exploring Slope (70-89), Unit Project (90-93), Looking Back and Looking Ahead (94-96) 16
18 Standard 5: Data Analysis, Probability, and Statistics Goal 5.1: Understand data analysis. Objective 1: 7.M Read and interpret tables, charts, and graphs, including frequency tables, scatter plots, broken line graphs, line plots, bar graphs, histograms, circle graphs, and stem-and-leaf plots. ( a) Objective 2: 7.M Explain conclusions drawn from tables, charts, and graphs. ( b) TG: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (16-43), Investigation 2: Analyzing Graphs and Tables (45-67), Investigation 4: Calculator Tables and Graphs (87-102), Stretching and Shrinking Investigation 2: Similar Figures (33-40, 49-52), Comparing and Scaling Investigation 2: Comparing Ratios, Percents, and Fractions (49), Investigation 4: Making Sense of Proportions (90), Accentuate the Negative Investigation 2: Adding and Subtracting Integers (53-56, 59-60), Moving Straight Ahead Investigation 1: Walking Rates (16-40), Investigation 2: Exploring Linear Functions With Graphs and Tables (42-65), Investigation 3: Solving Equations (67-94), Investigation 4: Exploring Slope (96-120), Unit Project ( ), Looking Back and Looking Ahead ( ) SE: Comparing and Scaling Investigation 4: Making Sense of Proportions (60), Data Distributions Investigation 1: Making Sense of Variability (5-27), Investigation 2: Making Sense of Measures of Center (25-54), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (55-73), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (74-85), Looking Back and Looking Ahead (86-88) TG: Comparing and Scaling Investigation 4: Making Sense of Proportions (91), Data Distributions Investigation 1: Making Sense of Variability (19-43), Investigation 2: Making Sense of Measures of Center (46-71), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (74-96), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (99-117), Looking Back and Looking Ahead ( ) SE: Data Distributions Investigation 1: Making Sense of Variability (5-27), Investigation 2: Making Sense of Measures of Center (25-54), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (55-73), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (74-85) 17
19 Objective 3: 7.M Use appropriate vocabulary and notations. ( c) Goal 5.2: Collect, organize, and display data. Objective 1: 7.M Collect, organize, and display data with appropriate notation in tables, charts and graphs, including scatter plots, broken line graphs, line plots, bar graphs, and stem-and-leaf plots. ( a) TG: Data Distributions Investigation 1: Making Sense of Variability (19-43), Investigation 2: Making Sense of Measures of Center (46-71), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (74-96), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (99-117) SE: Data Distributions Investigation 1: Making Sense of Variability (6-8, 27), Investigation 2: Making Sense of Measures of Center (54), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (60, 73), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (85), Looking Back and Looking Ahead (86-88) TG: Data Distributions Investigation 1: Making Sense of Variability (20-24, 42-43), Investigation 2: Making Sense of Measures of Center (71), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (83-88, 96), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (117), Looking Back and Looking Ahead ( ) SE: Data Distributions Investigation 1: Making Sense of Variability (5-27), Investigation 2: Making Sense of Measures of Center (25-54), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (55-73), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (74-85), Looking Back and Looking Ahead (86-88) TG: Data Distributions Investigation 1: Making Sense of Variability (19-43), Investigation 2: Making Sense of Measures of Center (46-71), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (74-96), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (99-117), Looking Back and Looking Ahead ( ) 18
20 Goal 5.3: Apply simple statistical measurements. Objective 1: 7.M Determine the measures of central tendency mean, median and mode with sets of data. ( a) Objective 2: 7.M Discuss distribution of data, including range, frequency, gaps, and clusters. ( b) Goal 5.4: Understand basic concepts of probability. Objective 1: 7.M Predict, perform, and record results of simple probability experiments. ( a) SE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (24), Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (55), Data Distributions Investigation 2: Making Sense of Measures of Center (25-54), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (55-73), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (76-77, 81, 83, 85) TG: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (41), Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (83), Data Distributions Investigation 2: Making Sense of Measures of Center (46-71), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (74-96), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values ( , ) SE: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (55), Data Distributions Investigation 1: Making Sense of Variability (12-15, 17, 20, 25, 27), Investigation 2: Making Sense of Measures of Center (46-71), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (55-73), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values (76-77, 83, 85) TG: Accentuate the Negative Investigation 3: Multiplying and Dividing Integers (83), Data Distributions Investigation 1: Making Sense of Variability (29-36, 38-43), Investigation 2: Making Sense of Measures of Center (46-71), Investigation 3: Comparing Distributions: Equal Numbers of Data Values (74-96), Investigation 4: Comparing Distributions: Unequal Numbers of Data Values ( , ) SE: What Do You Expect? Investigation 1: Evaluating Games of Chance (5-19), Investigation 2: Analyzing Situations Using an Area Model (20-37), Investigation 3: Expected Value (38-49), Investigation 4: Binomial Outcomes (50-60) 19
21 Objective 2: 7.M Recognize equally likely outcomes. ( c) Objective 3: 7.M Explain that probability ranges from impossible to certain (0% to 100%). Objective 4: 7.M Use the language of probability. ( b) Goal 5.5: Make predictions or decisions based on data. Objective 1: 7.M Make predictions based on simple theoretical probabilities. ( a) TG: What Do You Expect? Investigation 1: Evaluating Games of Chance (18-36), Investigation 2: Analyzing Situations Using an Area Model (38-58), Investigation 3: Expected Value (60-77), Investigation 4: Binomial Outcomes (79-94) SE: What Do You Expect? Investigation 1: Evaluating Games of Chance (5-19), Investigation 4: Binomial Outcomes (50-60) TG: What Do You Expect? Investigation 1: Evaluating Games of Chance (18-36), Investigation 4: Binomial Outcomes (79-94) SE: What Do You Expect? Investigation 1: Evaluating Games of Chance (14) TG: What Do You Expect? Investigation 1: Evaluating Games of Chance (34) SE: What Do You Expect? Investigation 1: Evaluating Games of Chance (19), Investigation 2: Analyzing Situations Using an Area Model (26), Investigation 3: Expected Value (49), Investigation 4: Binomial Outcomes (51-52, 60), Unit Project (61-62), Looking Back and Looking Ahead (63-65) TG: What Do You Expect? Investigation 1: Evaluating Games of Chance (35-36), Investigation 2: Analyzing Situations Using an Area Model (58), Investigation 3: Expected Value (76-77), Investigation 4: Binomial Outcomes (83-86, 94), Unit Project (96-104), Looking Back and Looking Ahead (94-95) SE: What Do You Expect? Investigation 1: Evaluating Games of Chance (5-19), Investigation 2: Analyzing Situations Using an Area Model (20-37), Investigation 3: Expected Value (38-49), Investigation 4: Binomial Outcomes (50-60) TG: What Do You Expect? Investigation 1: Evaluating Games of Chance (18-36), Investigation 2: Analyzing Situations Using an Area Model (38-58), Investigation 3: Expected Value (60-77), Investigation 4: Binomial Outcomes (79-94) 20
22 Objective 2: 7.M Use appropriate vocabulary and notations. ( b) SE: What Do You Expect? Investigation 1: Evaluating Games of Chance (19), Investigation 2: Analyzing Situations Using an Area Model (26), Investigation 3: Expected Value (49), Investigation 4: Binomial Outcomes (51-52, 60), Unit Project (61-62), Looking Back and Looking Ahead (63-65) TG: What Do You Expect? Investigation 1: Evaluating Games of Chance (35-36), Investigation 2: Analyzing Situations Using an Area Model (58), Investigation 3: Expected Value (76-77), Investigation 4: Binomial Outcomes (83-86, 94), Unit Project (96-104), Looking Back and Looking Ahead (94-95) Standards link: 21
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